1. Find the optimal March shipment schedule and its total transportation cost for each of the following: a. cotton b. polyester c. silk 2. The company will be opening a polyester-making department in the Nigeria mill. Although it will not be completed for several months, a current capacity of 1000 bolts for that fabric might be used during March for an added one-time cost of $2000. Find the new optimal shipment schedule and the total cost for that fabric. Should the Nigeria mill process polyester in March?3. Company learns that changes might have to be made to the March plans. If a new customer is obtained, the cotton demand in Manila and in Mexico City will increase by 10% at each location. Meanwhile, a big New York customer might cut back, which would reduce polyester demand by 10% in both New York and Chicago. Find the contingent optimal schedules and total costs (d) for cotton and (e) for polyester. 4. International Textile loses a profit of $10 for each bolt of cotton it falls short of meeting the distribution centre's demand. For polyester, the loss is $20 per bolt; for silk, it is a whopping $50 per bolt. By running the mills on overtime, the company can produce additional bolts at the additional costs shown in Table 4. Using only the original data from Tables 1 through 3 and the information in Table 4 (on next page), determine new production schedules to maximize overall profit successively for f. cotton g. silk Which fabric(s) and locations involve overtime production, and what are the overtime quantities? 5. Without making any calculations, offer the company other suggestions for reducing costs of transportation. Table 4 Overtime Production Costs ($) Cost per BoltMill Cotton Polyester SilkBahamas 10 10 N/AHong Kong 15 12 25Korea 5 8 22Nigeria 6 N/A N/AVenezuela 7 6 N/A